Due to the NP-hard nature of tensor decompositions [1]}, an approximate symmetric Tucker decomposition is often computed by higher-order eigenvector decomposition (HOEVD) [2]}.
It is the eigendecomposition of the flattened tensor and can be viewed as the symmetric version of higher-order singular value decomposition (HOSVD) [3]} and
sequentially truncated HOSVD [4]}.
Despite their popularity, HOSVD-based approaches offer no guarantee of returning critical points for the problem.
Recently, randomized projection methods have been applied to accelerate the procedure, see [5]}, [6]}, [7]}, [8]}, [9]} for state-of-the-art implementations of HOSVD.
But these methods may not be a good fit for the symmetric setting.
Also, they take the full tensor as input.
